A piggy bank contains 36 coins that consists of dimes and quarters totaling $5.85. How many quarters are in the piggy bank? In your final answer, include all necessary calculations.

D + q = 36

10d + 25q = 585

D is the number of dimes and Q is the number of quarters. There are 36 coins total in the piggy bank.

Each dime is worth 10 cents and each quarter is worth 25 cents, in some combination that totals 585 cents. I used cents instead of. 1 or 2.5 and 5.85 to make the calculations easier.

D + Q = 36 Solve the equation for D.

D = 36 - Q

10D + 25Q = 585

10 (36 - Q) + 25Q = 585 Substitute (36-Q) for D in this equation

360 - 10Q + 25Q = 585

360 + 15Q = 585

15Q = 225

Q = 15

There are 15 quarters.

If there are 15 quarters, then

D + Q = 36

D + 15 = 36

D = 21

There are 21 dimes.

Check your work!

21 x 10 = 210

15 x 25 = 375

210 + 375 = 585 cents or $5.85

There are 21 dimes and 15 quarters in the piggy bank.

Mr. Pacey

Teacher/Former JH Math Team Coach